In my experience, you put capital letter when you are pertaining to a deity or God. You also put capital letter in proper nouns. Therefore, grammatically speaking, I cannot find any basis to make it "Daddy". Since it is an essay, it is in the prerogative of the writer whether to capitalize the words or not. This is only my opinion, however.
– Lester NublaNov 15 '13 at 10:45